In the past decade, Artificial Intelligence driven drug design and discovery has been a hot research topic, where an important branch is molecule generation by generative models, from GAN-based models and VAE-based models to the latest diffusion-based models. However, most existing models pursue only the basic properties like validity and uniqueness of the generated molecules, a few go further to explicitly optimize one single important molecular property (e.g. QED or PlogP), which makes most generated molecules little usefulness in practice. In this paper, we present a novel approach to generating molecules with desirable properties, which expands the diffusion model framework with multiple innovative designs. The novelty is two-fold. On the one hand, considering that the structures of molecules are complex and diverse, and molecular properties are usually determined by some substructures (e.g. pharmacophores), we propose to perform diffusion on two structural levels: molecules and molecular fragments respectively, with which a mixed Gaussian distribution is obtained for the reverse diffusion process. To get desirable molecular fragments, we develop a novel electronic effect based fragmentation method. On the other hand, we introduce two ways to explicitly optimize multiple molecular properties under the diffusion model framework. First, as potential drug molecules must be chemically valid, we optimize molecular validity by an energy-guidance function. Second, since potential drug molecules should be desirable in various properties, we employ a multi-objective mechanism to optimize multiple molecular properties simultaneously. Extensive experiments with two benchmark datasets QM9 and ZINC250k show that the molecules generated by our proposed method have better validity, uniqueness, novelty, Fr\'echet ChemNet Distance (FCD), QED, and PlogP than those generated by current SOTA models.